№1 Вычислите: а) \(\frac{4}{9} \cdot \frac{3}{16}\) б) \(\frac{5}{9} : 4 \frac{1}{2}\) в) \(5 \cdot \frac{3}{25}\) г) \(1 \frac{1}{9} \cdot 18\) д) \(1 \frac{1}{8} : 2 \frac{2}{3}\) е) \(\frac{5}{8} : \frac{15}{16}\) ж) \(2 \frac{2}{5} : 6\) 3) \(8 \frac{4}{9}\) и) \(3 \frac{1}{2} : 1 \frac{3}{4}\)

Пошаговое решение:

1. а) \(\frac{4}{9} \cdot \frac{3}{16} = \frac{4 \cdot 3}{9 \cdot 16} = \frac{12}{144} = \frac{1}{12}\)
2. б) \(\frac{5}{9} : 4 \frac{1}{2} = \frac{5}{9} : \frac{9}{2} = \frac{5}{9} \cdot \frac{2}{9} = \frac{10}{81}\)
3. в) \(5 \cdot \frac{3}{25} = \frac{5 \cdot 3}{25} = \frac{15}{25} = \frac{3}{5}\)
4. г) \(1 \frac{1}{9} \cdot 18 = \frac{10}{9} \cdot 18 = \frac{10 \cdot 18}{9} = 10 \cdot 2 = 20\)
5. д) \(1 \frac{1}{8} : 2 \frac{2}{3} = \frac{9}{8} : \frac{8}{3} = \frac{9}{8} \cdot \frac{3}{8} = \frac{27}{64}\)
6. е) \(\frac{5}{8} : \frac{15}{16} = \frac{5}{8} \cdot \frac{16}{15} = \frac{5 \cdot 16}{8 \cdot 15} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3}\)
7. ж) \(2 \frac{2}{5} : 6 = \frac{12}{5} : 6 = \frac{12}{5 \cdot 6} = \frac{12}{30} = \frac{2}{5}\)
8. з) \(8 \frac{4}{9} = \frac{8 \cdot 9 + 4}{9} = \frac{72+4}{9} = \frac{76}{9}\)
9. и) \(3 \frac{1}{2} : 1 \frac{3}{4} = \frac{7}{2} : \frac{7}{4} = \frac{7}{2} \cdot \frac{4}{7} = \frac{7 \cdot 4}{2 \cdot 7} = \frac{4}{2} = 2\)